Tuesday, November 27, 2012

Analytic/Synthetic

Kant famously says (Critique of Pure Reason A7):

In all judgments in which the relation of a subject to the predicate is thought (if I only consider affirmative judgments, since the application to negative ones is easy) this relation is possible in two different ways. Either the predicate B belongs to the subject A as something that is (covertly) contained in this concept A; or B lies entirely outside the concept A, though to be sure it stands in connection with it. In the first case, I call the judgment analytic, in the second synthetic.

This relates to definitional mereotopology: Kant's claim is that analytic or explicative judgments are cases where, when B is predicated of A, B is a definitional part of A, and that synthetic or ampliative judgments are cases where, when B is predicated of A, B is definitionally relevant to A but not a definitional part of A, and A is not a definitional part of it. He says other things that can be taken mereotopologically, too, of course; for instance, that in (certain kinds of) synthetic judgments B is predicated of A because A and B are both parts of a whole, namely, the experiential unity combining them.

6 comments:

I find myself revisiting this most famous distinction perennially to try to descry some murky something in or beneath its more apparent clarity...but as a footnote to your post, what is it to be "definitionally relevant"? In synthetic a posteriori judgments such as "The house is red," how is the predicate relevant to the definition, rather then, say, being and accident whose sole connection or relevance to the subject is secured objectively, and thus in a manner external to the definition. It seems we must also say the same of Kant's interpretation of that other kind of synthetic judgment exemplified in the 'proposition' 7+5=12...what relevance does 5 have to the definition of 7?

I should also add in anticipation that it seems at least arguable to say 7 is "relevant" to the definition of 5 because it is CAN be included or comprehended in that definition of a unit counted seven times (or whatever be the appropriate definition), though this would seem to be relevancy only in potency (still, its not nothing). But red does not seem to enjoy the same relationship to house. What may be of additional interest is the fact that what accounts for this difference is not simply the distinction between apriori and a posteriori judgement --the syntheses are different in some other way, albeit one that might eventually have its source in this distinction...

'Definitional relevance' is purely a term of art in this context, defined by a set of topological properties (briefly noted at the link in the post), so I don't think much weight should be put on the 'definitional' part; here 'definitional relevance to X' means little more than 'having a connection to X, which we are considering in terms of how it is defined'. While all definitional parts are definitionally relevant to the subject term, not everything definitionally relevant to it is a definitional part. I'm not sure I fully follow the rest of your question. The relevant connection in the 7+5=12 case is not between 7 and 5 but between 7+5 and 12; the reason it's synthetic rather than analytic is that 12 is not a definitional part of 7+5 or any of its parts. But Kant himself answers your question about 'red' and 'house'; they are relevant to each other insofar as they are actually (not merely potentially) parts of an actual experiential whole.

I also think, incidentally, that we should beware of putting too much weight on the distinction itself in Kant, despite the length of his discussions on the subject; Kant is not inventing the distinction, but trying to pin down accurately the nature of Wolffian analysis, and then provide an alternative to it. The distinction matters much less than the gap in the philosophical discussion that Kant uses it to find.

Thanks for sorting out my rushed comment regarding Kant's famous 7+5=12...I was writing while prepping for a class; of course, the copula is to be translated from the "equals sign." That being said, I suppose the fundamental point I was trying to make escapes unscathed. Its sort of a thought experiment in its nascent stages, and maybe an unworthy one, but the fundamental idea is roughly that in this synthetic a priori proposition, though its connection is in no wise analytic, yet one may perceive in it a different synthetic relation than that of the synthetic a posteriori proposition "The house is red", and that this difference is not identical to the difference for which the apriori/a posteriori distinction accounts (though it may derive therefrom). I am still seeking clarity on this half-formed thought, but, specifically, what I mean is that, understanding definitional relevance as "having a connection to x", in the case of 7+5=12, there seems to be a *connection* of some sort that is unique: 12 is no part of the definition of 7+5, but some parts of the definition of 12 seem to be shared by the concept of 7+5, namely the counting unit. This may be stretch, since the operation of addition is foreign to the concept of 12 and essentially constitutive of 7+5, but then there is the question of whether the unit underlies the concept of this operation. As you can see, I am conflicted on the matter, presently. So much for the first issue.

Now to bring into relief the possible uniqueness of this connection I attempted to contrast it with that of the synthetic a posteriori "the house is red". There is no part of the definition of red that is shared by the "the house". The alleged "connection to x" in 7+5=12 is entirely absent from "The house is red". When you write"Kant himself answers your question about 'red' and 'house'; they are relevant to each other insofar as they are actually (not merely potentially) parts of an actual experiential whole."I think we are in agreement --at least as I am hearing you, the experiential whole is the object, whose actuality, according to the postulates of empirical thought, is dependent on its relation to sensiblity. But precisely here was the point I was trying to make: there is no potential relevance between red and house save through sensation; the only connection either IS or CAN BE discovered in the object actually given in sensation. The relevance between 7+5 and 12 is less meager, since they each seem to share the unit.

At least something broadly along these lines seems suggested by Kant himself, I think (around B12/B13), although he seems to want to tie it more closely to the a priori /a posteriori distinction, and doesn't seem to consider the difference mereologically, in terms of definitional overlap (or lack thereof), the way you are suggesting here.

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